Blending algorithm for trajectory planning

ABSTRACT

The present exemplary embodiment relates to motion control and planning algorithms to facilitate execution of a series of moves within a motion trajectory. In one example, a trajectory is specified as a sequence of one or more path segments. A velocity profile is calculated for each of the one or more path segments, wherein each velocity profile is divided into a blend-in region, a blend-out region and a remainder region. Each path segment is executed such that the blend-in region of its velocity profile overlaps only with the blend-out region of the previous profile.

BACKGROUND

The present exemplary embodiment relates to motion control and planningalgorithms. It finds particular application with increasing the accuracyand lowering execution time of trajectories by improving blendingbetween moves associated therewith. In one example, an algorithm isutilized to control the trajectory of a robot. However, it is to beappreciated that the present exemplary embodiment is also amenable toother like applications.

The production of goods generally includes movement in one or more axesto facilitate their assembly and manufacture. In one example, roboticsare employed to bring components to a product as it moves through anassembly process. In this manner, the robot picks up a component from anoffline tray and moves the component to an appropriate location on theproduct for assembly. The motion can involve rapid and precise movementto insure that production is accomplished at an optimum speed.

In some cases, the motion required from one location to another caninvolve specific obstacles that prevent the use of a direct path betweena start and end point. As a result, an indirect path must be employed.This indirect path can require the programming of a robot or otherautomated motion device to follow a path that avoids the obstacle whileminimizing the time lost in executing the full motion path. Typically,the path that is followed is comprised of a plurality of moves that areexecuted in series. Thus, the granularity of the motion path is easy tocontrol as there are an infinite number of moves that can be programmedto accomplish substantially any motion path.

To facilitate motion within a production environment, automated machines(e.g., robots) can be programmed with a set of instructions that dictatethe location, speed, path, etc, of their motion. These instructions canbe executed in succession based on instruction type, location within aninstruction set, priority, etc. Further, the instructions can be basedupon substantially any coordinate system such as a Cartesian coordinatesystem, a non-Cartesian coordinate system, a SCARA robot, a Delta robot,a cylindrical, a spherical, a polar, a picker, an articulated dependent,and an articulated independent joint space.

In addition, instructions can be executed in relation to an event withina motion profile. In one example, an instruction can be executed once aparticular parameter is met, such as an acceleration value. A moredetailed treatment of the creation and execution of motion instructionsis presented in Weinhofer, et al. (U.S. Pat. No. 7,180,253) which isincorporated in its entirety herein.

One difficulty with programming motion is transitioning between each ofthe plurality of disparate paths. A particular motion path (for examplea pick and place cycle) may require three different moves between astart and an end point. In this case, there are two points where motiontransitions between moves. The first transition is between the first andsecond move and the second transition is between the second and thirdmove. It is to be appreciated that if N is the number of moves in aparticular path, N−1 is the number of transition points associatedtherewith.

A blend radius can be employed to define the beginning and end of atransition. The blend radius can be expressed as the distance from amove's endpoint wherein the next move's instructions are simultaneouslyexecuted. Conventionally, there is no guarantee that blending will occuronly within the blend radius. Some combinations of move lengths andother move parameters can cause the moves to blend outside the blendradius which can cause undesired motion. In one example, the transitionwithin a second blend radius can occur before the transition in a firstblend radius has been complete which can cause undesired movement andassociated deleterious effects. Thus, what are needed are systems andmethods that facilitate accurate, rapid transitions between moves withinmotion applications.

BRIEF DESCRIPTION

The subject embodiments can be employed to produce smooth, jerk freecycles with minimal acceleration to carry a mass in a space. Utilizingthe improved algorithm described herein, an optimum number of pickcycles can be employed for robotic applications, such as a Delta robot,for example. Since the method of programming cycles is simple andflexible, it is extremely suitable for applications where pick-placecycle targets are varied because of integrated vision with conveyortracking.

In one aspect, a method is employed to generate a motion systemtrajectory. A trajectory is specified as a sequence of one or more pathsegments. A velocity profile is calculated for each of the one or morepath segments, wherein each velocity profile is divided into a blend-inregion, a blend-out region and a remainder region. Each path segment isexecuted such that the blend-in region of its velocity profile overlapsonly with the blend-out region of the previous profile.

In another aspect, a method is employed that generates a symmetricmotion trajectory. A path is symmetric if the path from a start point toan end point is identical to the path from the end point to the startpoint. A trajectory is specified as a sequence of one or more moves anda velocity profile is calculated for each of the one or more moves. Eachvelocity profile is divided into a blend-in region, a blend-out regionand a remainder region. The length of the blend-out regions for eachcurrent velocity profile are evaluated in view of the length of theblend-in regions for each subsequent profile. Both the deceleration andthe deceleration jerk of the current move are reduced, if the blend-outregion of the current move is the shorter than the blend-in region ofthe subsequent move to minimize the difference in duration of bothregions. Both the acceleration and the acceleration jerk of thesubsequent move are reduced if the subsequent blend region is shorterthan the current blend region, to minimize the difference in duration ofboth regions. A time offset is calculated and applied for the subsequentmove.

In yet another aspect, a method is employed to specify parameters of amotion trajectory algorithm. A path for motion is specified thatincludes at least two independent moves, a current move and a subsequentmove, the current move and subsequent move are defined on a rollingbasis as the motion trajectory is executed. A velocity profile iscalculated for each of the moves wherein each velocity profile isdivided into a blend-in region, a blend-out region and a remainderregion. The blend-out region of the profile of the current move and theblend-in region of the profile of the subsequent move are evaluated. Thestart time of the profile of the subsequent move is calculated. Ablending region is created that is comprised of the blend-in region ofthe profile of the current move and the blend-out region of the profileof the subsequent move to complete the trajectory.

The last three steps are repeated until the motion trajectory iscomplete.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a and 1 b illustrate motion trajectories comprised of aplurality of independent moves, in accordance with an exemplaryembodiment;

FIG. 2 a illustrates the concept of interchanging acceleration anddeceleration values for flipping around the time axis, in accordancewith an exemplary embodiment;

FIG. 2 b illustrates an asymmetric motion trajectory that includesvelocity limited moves utilizing a conventional motion algorithm, inaccordance with an exemplary embodiment;

FIG. 3 illustrates a motion trajectory that utilizes two blend radii, inaccordance with an exemplary embodiment;

FIG. 4 illustrates a motion trajectory that utilizes six blend radii, inaccordance with an exemplary embodiment;

FIG. 5 illustrates a motion trajectory that identifies the blend pointfor each of the two blend radii, in accordance with an exemplaryembodiment;

FIG. 6 illustrates the velocity of curves associated with each of thethree independent moves from the motion trajectory of FIG. 5, inaccordance with an exemplary embodiment;

FIG. 7 illustrates a motion trajectory wherein the blend radii are fiftypercent of the length of the shortest move along with the associatevelocity profile for each move therein, in accordance with an exemplaryembodiment;

FIG. 8 illustrates an asymmetric motion trajectory for back and forthmoves wherein the blend radii are one-hundred percent of the length ofthe shortest move utilizing a conventional algorithm, in accordance withan exemplary embodiment;

FIGS. 9 a, 9 b and 9 c illustrate the motion of a first move and asecond move and the velocity profiles associated therewith, utilizing aconventional algorithm in accordance with an exemplary embodiment;

FIG. 10 illustrates a move within a motion trajectory which is dividedinto three regions, a blend-in region, a blend-out region and aremainder region, in accordance with an exemplary embodiment;

FIG. 11 illustrates a velocity profile associated with the move of FIG.10, in accordance with an exemplary embodiment;

FIG. 12 illustrates the velocity profile of FIG. 11 that has beendivided into three regions, a blend-in region, a blend-out region and areminder region, in accordance with an exemplary embodiment;

FIG. 13 illustrates the velocity profiles of three successive moveswithin a motion trajectory wherein each successive move is not starteduntil the blend-out region of the previous move has been reached, inaccordance with an exemplary embodiment;

FIG. 14 illustrates the calculation of starting times for each of thethree moves as shown in FIG. 13 using the improved algorithm, inaccordance with an exemplary embodiment;

FIG. 15 illustrates a motion trajectory for back and forth moves whereinthe blend radii are equal to 100% of the length of the shortest moveutilizing an improved algorithm, in accordance with an exemplaryembodiment; and,

FIG. 16 illustrates the velocity profiles associated with the threemoves of FIG. 15, in accordance with an exemplary embodiment.

DETAILED DESCRIPTION

Standard blending algorithms can generate trajectories which are notsymmetric (e.g., trajectory from a start point to an end point is notthe same as that from the end point to a start point) and which do notalways stay close to their asymptotes. Blending starts when a profilereaches its blend point during its travel. Utilizing conventionalalgorithms, blending can begin at the point where a profile start todecelerate or at the point where a profile's remaining distance to go isless than a predefined limit. Such algorithms are dependent solely oninformation related to the currently executed move and are not concernedwith moves to be executed subsequently. As a result, the trajectory froma start point to an end point is typically different than the trajectoryfrom an end point to a start point. The improved algorithm, describedherein, removes such deficiencies by delaying the moment when blendingstarts by a predetermined time delay and/or adjusting the dynamics ofthe blend-in and blend-out regions.

The process works in two steps. During the first step, the blend-outregion of the first profile and the blend-in region of the secondprofile is evaluated. During the second step, the start time of thesecond profile is calculated, so that only the blend-in region of thefirst profile and the blend-out region of the second profile participatein blending and the whole trajectory completes in the shortest time.Typical examples of blending regions are: 1) a blend-out region of thefirst profile: its deceleration segment and a blend-in region of thesecond profile: its acceleration segment; 2) a blend-out region of thefirst profile: remaining distance to go is less than a blend radius anda blend-in region of the second profile wherein a command position isless than a blend radius; 3) a blend-out region of the first profile:remaining distance to go is less than fifty percent of first move'slength and a blend-in region of the second profile: a command positionis less than one-hundred percent of second move's length. If the moveconsists of more than two profiles, different formulas can be used forcalculation of blend-out and blend-in regions of each profile.

When the blending region for the two moves contains a minimum of a) theentire deceleration segment of the first move and b) the accelerationsegment of the second move, then the trajectory shape can be furtherimproved by using an optional additional step in the calculation of theprofile trajectories. The improvement is most noticeable, if the secondmove has higher command velocity than the first move and both moves arealmost collinear wherein jerk is specified as a percent of time.

First, the blend-in and blend-out regions are evaluated via conventionalmeans. Next, an additional optimization is made wherein after theinitial blend-in and blend-out regions are evaluated, the shorter one ischosen. If the blend-out region of the first move is the shorter one ofthe two, then both the deceleration and the deceleration jerk of thefirst move are reduced so that the difference in duration of bothregions is minimized (e.g., zero if possible). If the second move'sblend-in radius is the shorter one of the two, then both theacceleration and the acceleration jerk of the second move are reduced sothat the difference in duration of both regions is minimized (e.g., zeroif possible). A time offset of the second move is calculated andapplied.

FIG. 1 a illustrates a motion trajectory 100 that is comprised of threeindependent moves: a first move 102, a second move 104, and a third move106. The motion 100 can be employed with a “pick and place” motion thatis commonly utilized by robots in various manufacturing/productionapplications. In this example, the first move 102 is an Up Move; thesecond move 104 is a Horizontal Move; and the third move 106 is a DownMove. Move 102 has a start point 110 and a stop point 114. In thisexample, the start point 110 begins from zero velocity or rest. Once thefirst move 102 ends at 112, the second move 104 begins at 114 and endsat 116. Once the second move 104 ends, the third move 106 begins at 118and ends at 120 which is again at zero velocity. Since the moves in thisexample are executed independently and serially, there are no transitionpoints. In addition, although the first move 102 is orthogonal to thesecond move 104 and the second move is orthogonal to the third move 106,the moves can be at substantially any angle to each other and within anydimension.

FIG. 1 b illustrates a motion trajectory 200 that is comprised of sevenindependent moves: a first move 202, a second move 204, a third move206, a fourth move 208, a fifth move 210, a sixth move 212, and aseventh move 214. The start point of the first move 202 is from zerovelocity as is the end point of the seventh move 214. The sevenindependent moves in the trajectory 200 are executed serially whereinthe second move starts once the first move is complete and so on. It isto be appreciated that although the moves described herein are shown ina two-dimensional context, there is no limit to the number of dimensionsthat can be employed to define moves within a motion trajectory. Forexample, moves can be defined by N dimensions, where N is any positiveinteger greater than one.

FIG. 2 a includes four moves based on programmed acceleration anddeceleration values. An acceleration 252 and deceleration 254 areemployed for a first move; and an acceleration 258 and deceleration 256are employed for a fourth move. The acceleration 252 is equal to thedeceleration 256; and the deceleration 254 is equal to the acceleration258. The relative acceleration and deceleration values are also equalfor a second and a third move within the trajectory (not shown).

Regardless of the blending regions and the velocity profiles beingsymmetric, the trajectory from a start point to an end start point willbe the same as the trajectory from the end point to the start point ifthe above steps are followed. It is to be appreciated that the necessarycondition for generating a symmetric trajectory is that the velocityprofile must be flipped around its time axis when moving in the reversedirection. This can be achieved by either swapping its acceleration anddeceleration parameters or simply by using velocity profiles with equalacceleration and deceleration limits. This technique is known in the artand will not be discussed in detail herein.

FIG. 2 b illustrates a difficulty that occurs when executingtrajectories utilizing conventional algorithms. Many moves desired by aprogrammer are velocity-limited based on the move's length,acceleration, and deceleration values. Thus, as a move's length isdecreased, the maximum achievable velocity is also decreased. Utilizingconventional algorithms, acceleration and deceleration rates cannot becomputed to produce symmetric profiles if the moves are velocitylimited.

FIG. 3 illustrates a motion trajectory 300 that is comprised of threeindependent moves: a first move 302, a second move 304 and a third move306. This motion trajectory is very similar to the motion trajectory 100illustrated in FIG. 1. The main difference is that a blend radius isemployed to transition between each of the three independent moves.Blend radius 310 facilitates a transition between the first move 302 andthe second move 304. Blend radius 312 facilitates a transition betweenthe second move 304 and the third move 306.

The blend radii 310 and 312 are defined by a radius around the endpointof the initial move (e.g., 302 and 304 respectively) of the two movesthat require a transition between them. The motion trajectory variesbased on whether the motion lies inside or outside of the blend radius.Outside the blend radius, the trajectory exactly matches a programmedmove. Inside the blend radius, a smooth transition between moves isgenerated. It is to be appreciated that the smaller the blend radius,the sharper the corner and vice-versa.

The blended motion works in the following manner. The first move 302starts. When the first move 302 reaches the blend radius, the secondmove 304 is started wherein the first move 302 and the second move 304are executed simultaneously. Subsequently, the first move decelerates tozero at a predetermined time while the second move 304 continues. Thesuperposition of the first move 302 and the second move 304 within theblend radius generates a smooth transition between the first move 302and the second move 304. This sequence repeats for the transitionbetween the second move 304 and the third move 306 within the blendradius 312 to create another smooth transition.

Similarly, FIG. 4 illustrates an exemplary motion trajectory 400 that iscomprised of seven independent moves 402, 404, 406, 408, 410, 412, and414. This motion trajectory provides smooth transition points for themotion 400 via blend radii. Such motion blending provides an advantageover the trajectory illustrated in FIG. 1 b.

The motion trajectory 400 includes six blend radii 420, 422, 424 426,428, and 430 that are utilized to facilitate the transition of the firstmove 402 to the second move 404, the second move 404 to the third move406, and so on. As discussed in more detail below, the first and lastblend radii 420 and 430 can be one-hundred percent of the length of theshortest move being blended. This is an aspect that differs from anyintermediate blend radii (e.g., blend radii 422, 424, 426, and 428)which have a maximum size of fifty percent of the shortest move lengthbeing blended. These blend radii parameters can be employed to optimizeinstruction execution within a motion trajectory.

It is to be noted that the blend radii can be employed in substantiallyany location within a trajectory. Thus, blend radii may not be employeduntil the third move is reached in a motion trajectory. Alternatively orin addition, blend radii can stop being utilized five moves before themotion trajectory has ended. In this manner, the “start” and “stop”points that define blend radii usage are not necessarily related to thephysical beginning and end of a trajectory, which are generallyassociated with zero velocity. The successive moves that employ blendingwithin a trajectory are referred to as a blended motion sequence.

FIG. 5 illustrates a motion trajectory 500 that comprises threeindependent moves 502, 504, and 506 that are executed in relativesuccession to one another. A blend radius 508 is located between themoves 502 and 504 and a blend radius 510 is located between the moves504 and 506. The blend radius 508 begins at a blend point 514 and theblend radius 510 begins at a blend point 516. Blend points 514 and 516can be predetermined based on substantially any metric such as time,distance, velocity, acceleration, etc. In this embodiment, the blendpoints 514 and 516 are determined based on the velocity of each of themoves 502, 504, and 506.

In order to create the trajectory 500, a desired path for motion isinitially defined. This path can then be broken down into a plurality ofmotion segments (e.g., lines, circles, etc.). A velocity profile is thencalculated for each segment. Each velocity profile is divided into ablend-in region, a blend-out region, and a remainder region. Based uponthis allocation for each segment velocity profile, each path segment isstarted in such a way that the trajectory completes in minimal time butthe blend-in region of its velocity profile overlaps only with theblend-out region of the previous profile.

The blend radii 508 and 510 can serve two functions within an algorithm.First, the blend radii 508 and 510 control the trajectory curvature.Thus, a larger blend radius can result in a smoother trajectory. Second,the blend radii 508 and 510 control the cycle time. A larger blendradius means that the moves 504 and 506 start sooner since they run inparallel with the previous move. Thus, the entire trajectory 500 iscompleted more rapidly. As a result, the trajectory 500 speed is relatedto the size of the blend radii 508 and 510. The larger the diameter ofthe blend radii 508 and 510, the more quickly the trajectory iscompleted. In other words, when trajectory motion is outside a blendradius, only one move is executed. Alternatively, when motion is withina blend radius two moves are running concurrently wherein thesuperimposed outputs generate a smooth transition.

FIG. 6 illustrates three velocity profiles 610, 620, and 630 related toeach of the three moves 502, 504, and 506 within the time domain. It isto be appreciated that although the velocity is illustrated as atrapezoidal profile, it can be expressed as an S-curve, parabolic (orother polynomial), trigonometric, or other profile. Curve 610 representsthe velocity of the move 502; the curve 620 represents the velocity ofthe move 504; and the curve 630 represents the velocity of the move 506.The time domain is the same for all the curves 502, 504, and 506. Thus,the curve 610 (and move 502) is started prior to the curve 620 (move504) which is started prior to the curve 630 (move 506). In this manner,the moves 502-506 are partially superimposed upon one another to provideappropriate transition between moves and to speed the execution of thetrajectory 500.

The curve 610 increases in velocity from zero, a stationary position,until a maximum velocity is reached approximately midway through themove 502, wherein the acceleration is zero. Once the move 502 begins todecelerate, the second move 504 is started. At approximatelythree-quarters of the way through the move 504, the move deceleratesthereby initiating the third move 506. It is to be appreciated that theonly trigger for a successive move is when a blend region begins withina current move. Thus, there is no “look ahead” or mechanism beyond thedeceleration trigger for moves within a trajectory utilizingconventional algorithms.

The maximum achievable velocity for a move is based on the move'slength, acceleration, and deceleration values. For a velocity limitedmove, as a move length is decreased for a given aspect value (e.g.,acceleration, deceleration, etc.), the maximum achievable velocity isalso decreased.

FIG. 7 illustrates a trajectory 702 that utilizes a conventionalalgorithm. The trajectory 700 is shown as it relates to correspondingvelocity values for each of three moves 702, 704, and 706 includedtherein. A blend radius 710 is utilized between move 702 and 704 and ablend radius 712 is utilized between 704 and 706. The velocity profile720 illustrates the superposition of the moves as the trajectory 700 isexecuted, wherein successive moves are started before previous moveshave been completed. Generally, the conventional algorithm should notincrease the 710 and 712 blend radii above fifty percent of the shortestmove length of the two moves being blended to keep the trajectoryroughly symmetric.

FIG. 8 illustrates the trajectory 700 that utilizes a conventionalalgorithm wherein the blend radii 710 and 712 are equal to one-hundredpercent of the shortest move length. Since the blend radii 710 and 712are greater than fifty percent of the shortest move length, thetrajectory 700 is asymmetric, wherein motion in a first direction is notequivalent to motion in a second direction.

Optimally, the move 702 completes exactly when move 704 is at a distanceequal to the blend radius from its start point. If the move 702completes before the move 704, it does not harm the trajectory shape butthe profile may take more time to complete than necessary. However, ifthe move 702 completes after the move 704, the blend algorithm may getconfused. In one example, as illustrated in FIG. 9 a, the move 704completes before the move 702 completes. Consequently, the blendtrajectory is not tangential to the asymptotes.

FIG. 9 a illustrates the moves 702 and 704 within the trajectory 700wherein the blend radii 710 and 712 are equal to one-hundred percent ofthe shortest move length. FIGS. 9 b and 9 c illustrate the velocityprofiles associated with the moves 702 and 704 respectively. In thisexample, which utilizes a conventional algorithm, the start of the move704 is triggered by the first deceleration, 810, in the preceding move702. The move 704 is completed before the move 702, as indicated bypoint 812. Because of this situation, the trajectory 700 may not besymmetric when a blend radius is greater than fifty percent of the move702.

FIG. 10 illustrates an exemplary move 900 within a trajectory that isdivided in three non-overlapping regions to prevent asymmetrictrajectory motion. The three regions are: a blend-in region 910, ablend-out region 920 and a remainder region 930. The blend-in region 910is a part of a move that may participate in blending with previous move.Typically, it is located within a blend radius 940 from a move startpoint. The blend-out region 920 is the part of the move 900 that mayparticipate in blending with next move. Generally, it is located withinthe blend radius 950 from a move start point. The remainder 930 may notparticipate in any blending. Typically, it is located outside both theblend radii 940 and 950.

FIG. 11 shows a velocity profile 1000 that is associated with the move900. The velocity is shown in relation to time and is based upon thedesired distance, acceleration and deceleration parameters selected forthe move 900. It is to be appreciated that the velocity, acceleration,deceleration, and jerk parameters for each move can be independentlyselected. However, such random parameter combinations can slow downcycle time and produce poor velocity profiles. Therefore, in oneembodiment, parameters are modified so that the acceleration time of thenext move profile matches the deceleration time of the current moveprofile. It is to be appreciated that although the velocity isillustrated as a trapezoidal profile, it can be expressed as an S-curve,parabolic (or other polynomial), trigonometric, or other profile.

FIG. 12 shows the curve 1000 divided into three disparate regions, ablend-in region 1010, a blend-out region 1020, and a remainder region1030. In order to determine the appropriate velocity profile regions1010, 1020, and 1030, a conversion from distance units to time units isutilized. Such a conversion is known in the art and will not bediscussed in detail herein. In this manner, partitioning of the originalmove and partitioning of its velocity profile will be consistent. FIG.13 expands on this idea and illustrates starting successive moves andtheir associated velocity profiles 1110, 1120 and 1130. In order toprevent asymmetric and/or undesired motion, the blend-out region of thecurrent move blends only with blend-in region of the next move. In thismanner, remainders of both moves may not blend at all.

FIG. 14 shows the start times of successive moves in a trajectoryutilizing an improved blending algorithm. The correct timing of thisalgorithm is achieved by delaying the start of the next move by apredetermined amount of time. This time delay is calculated by theformula:ΔT(N)=max(0,T _(Blend-out)(N−1)−T _(Blend-in)(N))  (1)

where

T_(Blend-out)(N−1)=Duration of the blend-out region of move N−1

T_(Blend-in)(N)=Duration of the blend-in region of move N

ΔT(N)=Time delay of the start of the move N with respect to the start ofthe blend-out region of the move N−1

According to formula (1), the delay between the start of successivemoves within a trajectory is determined by a minimum time delay ΔT(N).It is to be appreciated that a longer delay can be employed, but thereis no reason since it slows down the execution of moves within atrajectory. This time delay is at least 0, to insure that a successivemove is not executed at least until the beginning of a blend-out regionof a previous move.

As shown, the velocity profile 1120 associated with a second move in atrajectory does not start until the blend-out region of the first move(velocity profile 1110) is reached. Similarly, the third curve 1130 doesnot begin until after a predetermined time delay beyond the start of theblend-out region of the second curve 1120. This algorithm makes noassumptions about the method used for calculation of the blend-in andblend-out region of each move. As an example, these regions can be basedon remaining move distance, or it can be based on remaining time, or itcan be based on command velocity. In addition, different methods can beemployed to calculate blend regions for each move within a trajectory.

FIG. 15 illustrates the use of this algorithm with a trajectory 1200that utilizes a blend radius 1210 and a blend radius 1220. Thistrajectory is based upon a three move motion that is illustrated in FIG.1, which includes moves 102, 104 and 106. The blend radius 1210 isrelative to the length of the moves 102 and 104 and the blend radius1220 is relative to the length of the moves 104 and 106. In each case,the blend radii 1210 and 1220 are defined as one-hundred percent of thelength of shortest of the two moves to which they correspond. Forexample, the blend radius 1210 is one-hundred percent of the length ofthe move 102, since that move is shorter than move 104.

For S-curves, this algorithm can be utilized to eliminate accelerationsteps and produce minimum finite jerk in the x and y direction. Asillustrated, the trajectory 1200 has a smooth profile for its x-axisvelocity 1230 and its y-axis velocity 1240 when utilizing S-curveprogramming. Additionally, the trajectory 1200 does not have anyacceleration steps in an S-curve domain as shown by the x-axisacceleration 1250 and the y-axis acceleration 1260. By eliminating suchacceleration steps, the motion path facilitates execution of high-speedprocesses.

Moreover, the algorithm allows complex motion to be defined by relativesimple motion segments. For example, trajectory 1200 shows a complexparabolic path that can be defined via a polynomial. Instead of firstdetermining the path that is desired (and the equation that defines sucha path), a user need only specify an up move, a horizontal move and adown move. More moves can be added as needed to avoid obstacles or othermachinery in a process. Once the individual segments are known, thetrajectory is created based on the acceleration and decelerationparameters and size of the blend radii for moves within a blended motionsequence.

FIG. 16 illustrates three S-curve velocity profiles 1310, 1320, and 1330that correlate the use of this algorithm with the trajectory 1200. Curve1310 is comprised of a one-hundred percent blend-out region and curve1330 is comprised of a one-hundred percent blend-in region. Curve 1320,which is executed between 1310 and 1330 and has only two regions, ablend-in and a blend-out. Since the algorithm does not allow blending tostart until the blend in-region of a successive move is reached, aone-hundred percent blend radius can be employed to facilitate fast,accurate motion with a minimum finite jerk.

The exemplary embodiment has been described with reference to thepreferred embodiments. Obviously, modifications and alterations willoccur to others upon reading and understanding the preceding detaileddescription. It is intended that the exemplary embodiment be construedas including all such modifications and alterations insofar as they comewithin the scope of the appended claims or the equivalents thereof.

1. A method for generating a motion system trajectory of an automatedmotion device with a processor having programming instructions stored ona computer readable medium for executing the method, comprising:specifying a trajectory as a sequence of path segments; calculating avelocity profile for each of the path segments; dividing each velocityprofile into a blend-in region, a blend-out region and a remainderregion; and executing each path segment by the automated motion devicesuch that the blend-in region of its velocity profile overlaps only withthe blend-out region of a previous velocity profile.
 2. The methodaccording to claim 1, wherein each segment is one of a line, a circle,an arc, and defined via a polynomial.
 3. The method according to claim1, wherein the dynamics of each velocity profile associated with eachpath segment are dependent on parameters of a current, the previous anda next segment within the motion trajectory.
 4. The method according toclaim 3, wherein the only the blend-in portion of the current segment isprocessed before the next path segment is executed.
 5. The methodaccording to claim 4, wherein the blend-out region of the currentsegment is not calculated until a pending instruction is received. 6.The method according to claim 1, wherein the dividing each velocityprofile into the blend-in and blend-out region depends on each segment'sorder within the sequence.
 7. The method according to claim 1, whereinthe path segments are executed sequentially.
 8. The method according toclaim 1, wherein the motion system trajectory is executed in one of aCartesian coordinate system, a non-Cartesian coordinate system, a SCARArobot, a Delta robot, a cylindrical, a spherical, a polar, a picker, anarticulated dependent, and an articulated independent joint space. 9.The method according to claim 8, wherein the motion system trajectory isbased on N dimensions, where N is an integer that is greater than
 1. 10.The method according to claim 1, wherein the blend-out region from acurrent move and the blend-in region from a successive move defines ablend radius.
 11. The method according to claim 10, wherein, thesuccessive moves that utilize the blend radius are a blended motionsequence, which starts at any location and stops at any location withinthe motion system trajectory.
 12. The method according to claim 11,wherein: the blend radii of a first and a last segment within theblended motion sequence are less than or equal to one-hundred percent ofa length of a smallest move length of the current move and thesuccessive move for all the moves within the blended motion sequence;and the blend radii for the segments between the first and the lastsegment within the blended motion sequence are less than or equal tofifty percent of the length of the smallest move of the current move andthe successive move for all the moves within the blended motionsequence.
 13. A method for generating a motion system trajectory of anautomated motion device, said method comprising: specifying a trajectoryas a sequence of path segments; calculating a velocity profile for eachof the path segments; dividing each velocity profile into a blend-inregion, a blend-out region and a remainder region; and moving saidautomated motion device in accordance with each of said path segments byexecuting each path segment in the automated motion device such that theblend-in region of its velocity profile overlaps only with the blend-outregion of a previous velocity profile.